Most apartments won't rent to you if you have a prior eviction, but how do they know about it unless you tell them?
There is no eviction registry they can check.
The best they can do is look at your credit report, but if your eviction was caused for reasons other than non-payment of rent, such as violating community rules, then where will be no clues there.
It's not like foreclosures where the only reason it happens is not making your mortgage payments, thus they always go on your credit report
An eviction from a rental can happen for a variety of reasons, and if it doesn't have to do with oweing your previous landlord any money, then there's nothing to report.